Study the following information carefully and answer the given questions.

The bar graph shows the number of hours required by different pipes to fill percentage part of a cistern.  

1) Pipe P, Q and R together started to fill the tank. After 7 hours pipe R closed and again after 3 hours Pipe P and Q are also closed. The remaining part is filled by pipe S in ‘n’ hours. find the value of n?

a) 7 hours

b) 9 hours

c) 10 hours

d) 12 hours

e) None of these

2) Pipe P, Q and R together started to fill a tank. After some time pipe Q and R closed (not necessary at the same time). Part filled by pipe Q is double of the part filled by pipe R. Pipe P opened for ‘t’ hours and fill the cistern completely. Find the value of ‘t’ if pipe Q opened only for 12 hours.     

a) 16 hours

b) 15 hours

c) 24 hours

d) 12 hours

e) None of these

3) Find which of the following pair of pipes takes a minimum number of hours to fill the tank completely? (Working together)

a) P & Q

b) P & T

c) R & S

d) Q & T

e) Q & S

4) Pipe P and S together started to fill the tank, but after 8 hours pipe P closed and pipe S alone fill the remaining cistern. If pipe P fills 300 litres per hour and pipe S fills 200 litres per hour. Find the capacity of the tank?

a) 2400litres

b) 3600litres

c) 7200 litres

d) 4800litres

e) None of these

5) Pipe P, Q and S started together to fill the tank. After 4 hours pipe Q closed and pipe T opened, with pipe P and S to fill the tank completely. After next ____ hour Pipe P and T both are closed. Now pipe S opened for ____ hour and fill the reaming part.

Which of the following options are possible for the blanks in the same order?

a) 6, 3

b) 6, 1

c) 5, 2

d) 4, 3.5

e) None of these

Answers :

1) Answer: B

Pipe P fills the tank completely in 40 hours. 

Pipe Q fills the tank completely in 30 hours.

Pipe R fills the tank completely in 60 hours.

Pipe S fills the tank completely in 30 hours.

Pipe T fills the tank completely in 25 hours. 

Let the total work = 120 units (LCM of 40, 30, 60 and 30)

Pipe P capacity = 3 units per hour

Pipe Q capacity = 4 units per hour

Pipe R capacity = 2 units per hour

Pipe S capacity = 4 units per hour

Part filled by pipe R in 7 hours= 7 x 2 = 14 units

Part filled by pipe P and Q in 10 hours = 10 x 7 = 70 units

Remaining part = 120 – (70+14) = 36 units

Number of hours required by Pipe S to fill the tank = 36/4 = 9 hours

2) Answer: A

Let the total work = 120 units (LCM of 40, 30 and 60)

Pipe P capacity = 3 units per hour

Pipe Q capacity = 4 units per hour

Pipe R capacity = 2 units per hour

Pipe Q’s 12 hour work = 4 x 12 = 48 units

As given Q does double the work done by pipe R.

Then pipe R does 24 units.

Remaining work = 120 – (48+24) = 48 units

48 units filled by pipe P in ‘t’ hours = 48/3 = 16 hours

3) Answer: D

Let the total work = 600 units (LCM of 40, 30, 60, 30 and 25)

Pipe P capacity = 15 units per hour

Pipe Q capacity = 20 units per hour

Pipe R capacity = 10 units per hour

Pipe S capacity = 20 units per hour

Pipe T capacity = 24 units per hour

The pair which does the maximum number of units per hour will take a minimum number of the hour.

P+Q = 35 units/hour

P+T = 39 units/hour

R+S = 30 units/day

Q+T = 44 units/day

Q+S = 40 units/day

Hence pair of pipe Q and T fill the tank in minimum time.

4) Answer: C

Let the total capacity = 120 units (LCM of 40 & 30)

Pipe P capacity = 3 units per hour

Pipe S capacity = 4 units per hour

Pipe (P+S)’s 8 hours work = 7 x 8 = 56 units

Remaining work = 120 – 56 = 64 units

Pipe S alone fill 64 units in = 64/4 = 16 hours

Total part filled by Pipe P = 8 x 300 = 2400 litres

Total part filled by Pipe S = (16+8) x 200 = 24 x 200 = 4800 litres

Total Capacity = 2400 + 4800 = 7200 litres

5) Answer: C

Let the total work = 600 units (LCM of 40, 30, 30 and 25)

Pipe P capacity = 15 units per hour

Pipe Q capacity = 20 units per hour

Pipe S capacity = 20 units per hour

Pipe T capacity = 24 units per hour

Part filled by pipe P, Q and S in 4 hours = (15 + 20 + 20) x 4= 220 units

Remaining work = 600 – 220 = 380 units

Now, after X hours Pipe P and T both closed and pipe S opened for Y hours to fill the tank.

Then, (15+ 20 + 24) x X + 20 x Y= 380

59X +20Y = 380

None of the given option satisfies the equation, hence option E is answer.